Recently, thanks to micro-fabrication technique of sub-microns, LSI (Large-Scale Integration) of higher degree of integration has been developed and, as a result, it becomes possible to pack functions that have been conventionally implemented in a plurality of separate packages in one LSI. Conventional QFP (Quad Flat Package) and PGA (Pin Grid Array) can no longer accommodate the increased number of pins resulting from incorporating necessary functions in one package and, therefore, LSIs of BGA (Ball Grid Array) or CSP (Chip Size Package) in particular come to be used these days. Further, for applications requiring micro-miniaturization such as portable telephones, BGA package is used even if the number of pins is not so large.
Though BGA and CSP packages of LSI much contribute to micro-miniaturization, after assembly, soldered portions and the like are not visible from the appearance. Therefore, when printed boards and the like mounting BGA and CSP packages are to be inspected, the object of inspection is irradiated with X-ray, and the acquired fluoroscopic image is analyzed, for determining whether the quality is acceptable or not.
By way of example, Patent Document 1 discloses an X-ray tomographic surface inspection apparatus that can acquire a sharp X-ray image by using an X-ray plane sensor.
Patent Document 2 discloses a method for reconstructing an image in inclined-three-dimensional X-ray CT (Computed Tomography) by arbitrarily selecting an angle of X-ray irradiation.
Patent Document 3 discloses an X-ray inspection device in which two-dimensional inspection is performed based on X-ray images acquired by a parallel X-ray detection device, and three-dimensional inspection is performed based on X-ray images acquired by inclined X-ray detecting means, so that both inspections can be done at high speed. A technique of reconstructing a three-dimensional image of an object of inspection based on a plurality of X-ray images is also mentioned in this reference. As a method for reconstruction, “filtered back-projection method” is suggested.
Further, Patent Document 4 discloses a mechanism that can be driven by a single motor to move an X-ray source on linear orbit, circular orbit and spiral orbit for taking laminography in an X-ray tomographic apparatus. Here, the X-ray source is moved, and since the X-ray source is heavy and only one motor is used for driving, high-speed movement is difficult. Further, in order to realize three different moving modes of rotational, linear and spiral movements by one imaging system, the mechanism is complicated. Since various improvements of the mechanism are required to increase the speed of movement, it is difficult to increase the operation speed of the mechanism.
In a general industrial X-ray fluoroscope, if the object of inspection is of minute size, it is desirable to acquire an X-ray fluoroscopic image enlarged as much as possible. For this purpose, the size of focal point as the area of X-ray generation must be extremely small. Thus, a micro-focus X-ray source, which is a transmission type X-ray source having the focal point dimension of a few μm, is used. If an electron beam current (X-ray source current) for generating the X-ray is increased in such a micro-focus X-ray source in order to improve image quality of the fluoroscope, heat builds up at a portion of the target where the electrons impinge (focal point) and the target melts locally. Therefore, it is a common practice to set an allowable limit value (permissible load). Patent Document 5 discloses a micro-focus X-ray source including an anode (target) consisting of a rotating disk, enabling increase of the permissible load.
Patent Document 6 discloses a pulse X-ray source capable of generating pulsed X-rays by intermittently defocusing the electron beam using a deflecting electromagnetic coil, to make longer the life of X-ray source.
[Method for Image Reconstruction of X-Ray CT]
As described above, in X-ray CT, based on the measured values of X-ray after transmission through the object and detected by the X-ray detector, at least a cross-sectional image of the object is reconstructed. Since three-dimensional distribution of X-ray absorption factor of the object or at least a part of the object can be obtained, it is eventually possible to reconstruct an arbitrary cross-sectional image of the object or a part of the object, that is, an image of a plane that crosses the light receiving surface of the X-ray detector. As the method for reconstruction, “analytical method” and “iterative method” have been known. In the following, these methods for image reconstruction will be briefly discussed.
(Description of X-Ray Projection Data)
FIG. 57 is an illustration related to the methods for image reconstruction. The X-ray image reconstruction refers to a method for calculating distribution of X-ray absorption coefficient in an object of inspection, by measuring, from a plurality of different angles, how much X-ray irradiating the object from outside is absorbed (attenuated) by the object of inspection.
In the following, description will be given assuming that measurement is done using a so-called scanning X-ray source.
Referring to FIG. 57, X-ray emitted from an X-ray focal point Fa corresponding to an X-ray detector Da passes through an object of inspection (not shown) and reaches a pixel Pa of X-ray detector Da. As the X-ray is transmitted through the object of inspection, the amount of X-ray (X-ray intensity) attenuates by the amount corresponding to X-ray absorption coefficient of each of the components and the like forming the object of inspection. The amount of attenuation in X-ray intensity is recorded as a pixel value of detector pixel Pa.
When we represent the X-ray intensity emitted from X-ray focal point Fa by I, the path of X-ray from X-ray focal point Fa to detector pixel Pa by t and the distribution of X-ray absorption coefficients of the object of inspection by f(x, y, z), the intensity Ia of X-ray that reached the detector pixel Pa is given by the following equation (1).Ia=I×exp{−∫f(x,y,z)dt}  (1)
Taking the logarithm of both sides of the equation above, distribution of X-ray absorption coefficients along the path t is given as a linear integral value of Equation (2) below. A value obtained by measuring the X-ray absorption coefficients distribution by the X-ray detector is referred to as projection data. Specifically, the X-ray detector detects a distribution of X-ray attenuation (or X-ray intensity distribution).∫f(x,y,z)dt=ln(I/Ia)  (2)
(Description of Analytical Method (for Example, FBP Method: Filtered Back-Projection Approach))
As shown in FIG. 57, when the analytical method is used, for one object of inspection (or one part of the object of inspection), projection data of X-ray intensity Ib of the X-ray emitted from a focal point Fb and reached an X-ray detector Db, which is arranged at a position different from the arrangement of X-ray detector Da, is detected. In actual practice, the projection data as such is detected for a plurality of arrangements with respect to one object of inspection (or one part of the object of inspection), and a cross-sectional image of the object of inspection is reconstructed from the projection data.
FIG. 58 shows the arrangements of a field of view FOV and a reconstruction pixel V as the object of reconstruction operation in the field of view FOV of the object of inspection, X-ray focal points Fa and Fb, and X-ray detectors Da and Db shown in FIG. 57, viewed from above. When the X-ray that has been transmitted through a portion of reconstruction pixel V forms images on X-ray detectors Da and Db, the images are enlarged in proportion to the ratio of (distance from focal point to reconstruction pixel V) to (distance from focal point to X-ray detector).
Feldkamp et al. propose a reconstruction algorithm for three-dimensional image reconstruction based on Equation (2). The algorithm (a so-called Feldkamp method) is well known as disclosed in Non-Patent Document 1 and, therefore, detailed description will not be given here. In the following, Filtered Back-Projection method as a general method will be briefly described.
An operation of obtaining the distribution f(x, y, z) of X-ray absorption coefficients from the projection data, by adding projection data along the path t followed by the X-ray is referred to as back-projection. If the projection data are simply added, blurring occurs because of peaked point spread function of imaging system and, therefore, the projection data are filtered. Here, a high-frequency emphasizing filter, such as Shepp-Logan filter, is used for the filtering. The desirable direction of filtering is considered to be vertical to the direction of X-ray transmission path. In Feldkamp method, filtering is done approximating that projection data transmission paths are all in the same direction, and an image allowing inspection can be reconstructed.
In the following, steps of image reconstruction in accordance with the present embodiment will be described. First, a value pa′ obtained by filtering the projection data pa of detector pixel. Pa at X-ray detector Da is added to a pixel value v of reconstruction pixel V. Further, a value pb′ obtained by filtering the projection data pb of detector pixel Pb at X-ray detector Db is added to the pixel value v of reconstruction pixel V. Then, we obtain v=pa′+pb′. When such a back-projection operation is conducted on all or some of the X-ray detectors, the pixel value v of eventually resulting reconstruction pixel V will be represented by Equation (3) below:ν=Σ(pa′+pb′+ . . . )  (3)
By performing this operation for all the reconstruction pixels V in the reconstruction area (field of view) FOV, the distribution of X-ray absorption coefficients of the object of inspection is obtained, and hence, a reconstructed image data is obtained.
FIG. 59 is a flowchart representing the process steps of the Filtered Back-Projection method.
Referring to FIG. 59, when the process in the analytical method starts (S5002), first, projection data to be the object of processing are selected from projection data of a plurality of picked-up images (S5004). Next, the selected projection data are filtered (S5006).
Further, not-yet processed reconstruction pixel V in reconstruction field of view FOV is selected (S5008), and a detector pixel for the reconstruction pixel V is found (S5010).
Thereafter, the filtered pixel value is added to reconstruction pixel V (S5012), and whether or not addition has been done on all reconstruction pixels is determined (S5014). If the process is not yet done on all reconstruction pixels, the process returns to step S5008, and if the process has been completed, the process proceeds to step S5016.
At step S5016, whether or not the process has been done on all projection data is determined. If the process is not yet done on all projection data, the process returns to step S5004. If the process has been done on all projection data, generation of a reconstructed image ends (S5018).
(Description of Iterative Method (SART))
In the iterative method, the distribution f(x, y, z) of X-ray absorption coefficients and the projection data In (I/Ia) of the object of inspection are regarded as equations for reconstruction.
FIG. 60 is a schematic illustration showing the concept of the process in accordance with the iterative method, when a scanning X-ray source is used. FIG. 61 corresponds to the illustration of FIG. 60, viewed from above.
Referring to FIGS. 60 and 61, the steps of reconstruction in accordance with the iterative method will be described. A vector ν (with an overhead arrow→representing a vector; in the text of specification, represented by “ν”) obtained by arranging a series of pixel values of the reconstructed image and a vector p (with an overhead arrow→representing a vector; in the text of specification, represented by “p”) obtained by arranging a series of projection data are represented by Equations (4) and (5) below.
In the following, a pixel of an image calculated to be formed on X-ray detector Da by the X-ray emitted from X-ray focal point Fa assuming that the reconstruction pixel V has a certain value is referred to as an intermediate projection pixel Qa, while the pixel actually observed on X-ray detector Da is referred to as detector pixel Pa. Similarly, corresponding pixels of X-ray detector Db will be referred to as intermediate projection pixel Qb and detector pixel Pb.
In the iterative method, for the assumed reconstruction pixel vector ν and the corresponding intermediate projection data vector q, iterative operation of updating the assumed vector ν is continued until the intermediate projection data vector q can be regarded as matching the projection data of actually measured detector pixel value Pa or Pb, and thereby, the solution ν is obtained.{right arrow over (ν)}=(ν1,ν2, . . . , νJ)T  (4){right arrow over (p)}=(p1,p2, . . . , pI)T  (5)
Here, J represents the number of pixels in the reconstruction area (field of view), and I represents the number of pixels of the projection data. Further, T represents transposition. A projection operation establishing a relation between ν and p is given by the I×J coefficient matrix of (6).W={wij}  (6)
Here, the image reconstruction in accordance with the iterative method can be formulated as a problem of solving the linear equation (7) below to find the solution ν.W{right arrow over (ν)}={right arrow over (p)}  (7)
Specifically, the contribution of vj to pj is wij. It is noted that W represents how much the pixel value ν of the reconstructed image contributes to the pixel value p of projection data. It can be calculated from geometric positions of the X-ray focal point and the X-ray detector, and this value is sometimes referred to as a detection probability or weight.
As the iterative method, a method for algebraically solving the equation or a method considering statistical noise have been proposed. In the following, a commonly used algebraic method for SART (Simultaneous Algebraic Reconstruction Technique) will be described. Details are described in Non-Patent Document 2.
In SART, first, an initial reconstructed image ν0 (with an overhead arrow→representing a vector; in the text of specification, represented by “ν0”) given by the following expression is assumed.{right arrow over (ν)}0  (8)
The initial reconstructed image ν0 may be data of all 0, or it may assume data obtained from CAD (Computer Aided Design) data.
Next, an intermediate projection data q0 (with an overhead arrow→representing a vector; in the text of specification, represented by “q0”) given by the following equation (9) is generated, using projection operation W.{right arrow over (q)}0=W{right arrow over (ν)}0  (9)
The intermediate projection data q0 may be generated for one projection data, or it may be generated for a plurality of projection data. In the following, description will be given assuming that the generation is performed for one projection data.
The generated intermediate projection data q0 is compared with projection data p obtained from the X-ray detector. As the method for comparison, a method for calculating difference and a method for performing a division are known. In SART, the difference (p−q0) is calculated.
The initial reconstructed image ν0 is updated. The equation used for updating (iteration equation) is as represented by (10) below.
                              v          j          1                =                              v            j            0                    +                                                    ∑                                  i                  =                  1                                I                            ⁢                                                          ⁢                                                                                          p                      i                                        -                                          q                      i                                                                                                  ∑                                              j                        =                        1                                            J                                        ⁢                                                                                  ⁢                                          w                      ij                                                                      ⁢                                  w                  ij                                                                                    ∑                                  i                  =                  1                                I                            ⁢                                                          ⁢                              w                ij                                                                        (        10        )            
Further, the time required for updating calculation can be made shorter by calculating in advance the elements (11) and (12) appearing in Equation (10).
                              ∑                      i            =            1                    I                ⁢                                  ⁢                  w          ij                                    (        11        )                                          ∑                      j            =            1                    J                ⁢                                  ⁢                  w          ij                                    (        12        )            
The reconstructed image generated by the calculation above is input as the initial image, and the same process is repeated for a number of times, whereby the data of the reconstructed image can be obtained.
FIG. 62 is a flowchart representing the process in accordance with the iterative method.
Referring to FIG. 62, when the process in accordance with the iterative method starts (S5102), the initial reconstructed image is set (S5104). As described above, all values may be 0, in the initial reconstructed image. Next, among a plurality of projection data corresponding to positions of a plurality of X-ray detectors, projection data to be the object of processing is selected (S5106).
Intermediate projection data is generated. The method for generating the intermediate projection data is as described above.
Then, not-yet-processed reconstruction pixel V in reconstruction field of view FOV is selected (S5110).
A detector pixel corresponding to the reconstruction pixel is found (S5112).
Based on the iteration equation, the value of reconstruction pixel V is updated (S5114).
Next, whether or not updating of all reconstruction pixels has been done is determined (S5116). If the process is not finished on all reconstruction pixels, the process returns to S5110. On the other hand, if the process has been finished, the flow proceeds to step S5118.
At S5118, it is determined whether or not the process has been done on all projection data. If the process is not yet finished for all projection data, the process returns to step S5106. If the process has been done on all projection data, the process proceeds to step S5120.
At S5120, it is determined whether the process has been repeated for a defined number of iterations. If not yet repeated, the process returns to step S5104 and the process is repeated using the present reconstruction pixel value as the initial reconstructed image, and if the process has been repeated for the defined number of iterations, the generation of reconstructed image ends (S5022).
As described above, a three-dimensional image of the object of inspection can be reconstructed from the projection data acquired by the X-ray detector.
In the analytical method, however, it is desired to maintain a constant relation of relative arrangement between the X-ray focal point and the X-ray detector even if the relative positions of the X-ray detector, the focal point and the object are changed to get each of the plurality of projection data, considering ease of computation when filtering is applied to each pixel of the X-ray detector. In other words, when the X-ray detector is viewed from the focal point, it is desirable that the positional relation between the focal point and the X-ray detector is kept constant, even if the angle of a portion included in the field of view of the object within the visible solid angle and/or position in the object may vary. Further, when the back-projection method is applied, it is desired that the plurality of projection data of portions included in the field of view of the object are acquired at every equal angle, in order to reduce artifact and the like.
In contrast, the iterative method does not involve any such limitation regarding the relative arrangement between the X-ray focal point and the X-ray detector.
Patent Document 1: Japanese Patent Laying-Open No. 2000-46760
Patent Document 2: Japanese Patent Laying-Open No. 2003-344316
Patent Document 3: Japanese Patent Laying-Open No. 2006-162335
Patent Document 4: Japanese Patent Publication No. 5-86218
Patent Document 5: Japanese Patent Laying-Open No. 2001-273860
Patent Document 6: Japanese Patent Laying-Open No. 2005-347174
Non-Patent Document 1: L. A. Feldkamp, L. C. Davis and J. W. Kress, “Practical cone-beam algorithm,” Journal of the Optical Society of America. A, 612-619 (1984)
Non-Patent Document 2: A. H. Anderson and A. C. Kak, “SIMULTANEOUS ALGEBRAIC RECONSTRUCTION TECHNIQUE (SART): A SUPERIOR IMPLEMENTATION OF THE ART ALGORITHM,” ULTRASONIC IMAGING 6, 81-94 (1984)